In this chapter, you will consider the force of gravity:

Transcription

1 Gravity Chapter 5

2 Guidepost In this chapter, you will consider the force of gravity: What were Galileo s insights about motion and gravity? What were Newton s insights about motion and gravity? How does gravity explain orbital motion? How does gravity explain tides? What were Einstein s insights about motion and gravity?

3 5-1 Galileo s and Newton s Two New Sciences Galileo provided key information that helped Newton understand gravity Space stations and astronauts, as well as planets, moons, stars, and galaxies, follow paths called orbits that are described by three simple laws of motion and a theory of gravity first understood by Isaac Newton..

4 Isaac Newton ( ) Added physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo, and Kepler Invented calculus as a necessary tool to solve mathematical problems related to motion Discovered the three laws of motion Discovered the universal law of mutual gravitation

5 Galileo s Observations of Motion Acceleration of gravity: 9.8 m/s 2 Galileo found that a falling object is accelerated downward. Each second its velocity increases by 9.8 m/s ( 32 ft / s ).

6 Galileo s Observations of Motion (cont d.) The acceleration of gravity is independent of the mass (weight) of the falling object (a) According to a traditional story, Galileo demonstrated that the acceleration of a falling body is independent of its weight by dropping balls of iron and wood from the Leaning Tower of Pisa. In fact, air resistance would have confused the result.

7 Newton s First Law of Motion A body continues at rest or in uniform motion in a straight line unless acted upon by some net force An astronaut floating in space will continue to float forever in a straight line unless some external force is accelerating him/her.

8 Newton s Second Law of Motion The acceleration (a) of a body is inversely proportional to its mass (m), directly proportional to the net force (F), and in the same direction as the net force

9 Newton s Third Law of Motion To every action, there is an equal and opposite reaction The same force that is accelerating the boy forward, is accelerating the skateboard backward.

10 How Do We Know? 5-1 Cause and effect Ancient philosophers argued that objects moved because of tendencies Newton s second law of motion (F=ma) was the first clear statement of the principle of cause and effect That is, effect (a) must be the result of a cause (F) Without cause and effect, we could never expect to understand how nature works

11 Mutual Gravitation The inverse square law Any two bodies are attracting each other through gravitation, with a force (F) proportional to the product of their masses (M,m) and inversely proportional to the square of their distance (r) F = GMm r 2

12 Understanding Orbital Motions Universal mutual gravitation allows us to understand orbital motion of planets and moons For example, Earth and the moon attract each other through gravitation Earth is much more massive than the moon, thus, Earth s gravitational force constantly accelerates the moon towards Earth This acceleration is constantly changing the moon s direction of motion, holding it on its almost circular orbit

13 5-2 Orbital Motion and Tides In order to stay on a closed orbit, an object has to be within a certain range of velocities (a) According to a traditional story, Galileo demonstrated that the acceleration of a falling body is independent of its weight by dropping balls of iron and wood from the Leaning Tower of Pisa. In fact, air resistance would have confused the result.

14 Geosynchronous Orbits A geosynchronous satellite orbits eastward with the rotation of Earth and remains above a fixed spot on the equator, which is ideal for communications and weather satellites

15 Orbital Velocity An object s circular velocity is the lateral velocity it must have to remain in a circular orbit. If mass of the spaceship << the mass of Earth, then the circular velocity is V c = GM r M = mass of the central body in kg G = gravitational constant (6.67ˣ10-11 m3/s2/kg) r = orbital radius

16 Calculating Escape Velocity Escape velocity is the velocity required to escape an astronomical body If mass of the spaceship << the mass of Earth, then the circular velocity is V e = 2GM r M = mass of the central body in kg G = gravitational constant (6.67ˣ10-11 m3/s2/kg) r = radius of the central body

17 Common Misconception Misconception: There is no gravity in space Truth: Space is filled with gravitational forces from Earth, the Sun, and all other objects in the Universe A weightless astronaut in space is actually falling along a path due to the combined gravitational fields Just above Earth s atmosphere, the orbital motion of is almost completely due to Earth s gravity

18 Newton s Version of Kepler s Third Law Balancing the force (called centripetal force ) necessary to keep an object in circular motion with the gravitational force P 2 = 4π2 GM r 3 An expression equivalent to Kepler s third law P years2 = a AU 3

19 Tides and Tidal Forces Caused by the difference of the Moon s gravitational attraction on the water on Earth (a) Tides are produced by small differences in the gravitational force exerted on different parts of an object. The side of Earth nearest the Moon is subject to a larger force than Earth s center, and that is subject to a larger force than the side farthest from the Moon. Relative to Earth s center, small forces are left over, and they cause tides.

20 Spring and Neap Tides The Sun is also producing tidal effects, about half as strong as the Moon Near Full and New Moon, those two effects add up to cause spring tides Near first and third quarter, the two effects work at a right angle, causing neap tides

21 Common Misconception Misconception: The Moon s effect on tides means that the Moon has an affinity for water, including the water in your body, and that s how the Moon affects you Truth: the Moon s gravity acts on all of Earth, the rock as well as the water, producing tidal bulge in the near- and far-side ocean as well as the rocky surface

22 Acceleration of the Moon s Orbital Motion Earth s tidal bulges are slightly tilted in the direction of Earth s rotation Gravitational force pulls the moon slightly forward along its orbit (c) Tides can alter both an object s rotation and its orbital motion.

23 Astronomy After Newton Newton s Principia (1687) changed astronomy, changed science, and changed the way people think about math and nature Clearly demonstrated the power of mathematics as a language of precision for the study of nature Showed that the rules that govern the Universe are simple

24 How Do We Know? 5-2 Hypotheses can explain past events or can predict what will be found if we explore further If a prediction of a hypothesis is confirmed, scientists gain confidence that the hypothesis Prediction can point the way to unexplored avenues of knowledge e.g., the Standard Model regarding atomic particles and the forces between them confirmed previous observations

25 5-3 Einstein and Relativity Einstein ( ) Noticed that Newton s laws of motion are only correct in the limit of low velocities (<<speed of light) leading to his theory of special relativity Also revised the understanding of gravity leading to his theory of general relativity

26 The First Postulate of Relativity The principle of relativity The laws of physics are the same for all observers, no matter what their motion, as long as they are not accelerated (a) The principle of relativity says that observers can never detect their uniform motion, except relative to other objects. Neither of these travelers can decide who is moving and who is not.

27 The Second Postulate of Relativity The constant speed of light The speed of light in a vacuum is constant and will have the same value for all observers independent of their motion relative to the light source

28 The Theory of Special Relativity The first two postulates describe the theory of special relativity Observed mass of a moving particle depends on its velocity The energy of a body at rest 0 Instead, we find E = m 0 c 2

29 Effects of Special Relativity The observed mass of moving electrons depends on their velocity. As the ratio of their velocity to the velocity of light, v/c, increases, the mass of the electrons relative to their mass at rest, m/m 0, increases. Such relativistic effects are quite evident in particle accelerators, which accelerate atomic particles to very high velocities.

30 The Third Postulate of Relativity The general theory of relativity The equivalence principle: new description of gravity Observers cannot distinguish locally between inertial forces due to acceleration and uniform gravitational forces due to the presence of a massive body

31 Inertia and Acceleration in a Spaceship (a) An observer in a closed spaceship on the surface of a planet feels gravity. (b) In space, with the rockets smoothly firing and accelerating the spaceship, the observer feels inertial forces that are equivalent to gravitational forces.

32 Confirmation of the Curvature of Space-Time: Mercury s Perihelion (a) Mercury s orbit precesses arc seconds per century faster than predicted by Newton s laws. (b) Even when you ignore the influences of the other planets, Mercury s orbit is not a perfect ellipse. Curved space-time near the Sun distorts the orbit from an ellipse into a rosette. The advance of Mercury s perihelion is exaggerated by a factor of about one million in this figure.

33 Confirmation of the Curvature of Space-Time: Deflection of Sunlight Like a depression in a putting green, the curved space-time near the Sun deflects light from distant stars and makes them appear to lie slightly farther from the Sun than their true positions.

34 Discussion Questions When a person says he gained weight, does he mean that he gained in mass, gravity, or both mass and gravity? Hint: F = ma, where force = weight and a = acceleration due to gravity People who lived before Newton may not have believed in cause and effect as strongly as you do. How do you suppose that affected how they saw their daily lives?